Answer :
Sure! Let's simplify the expression [tex]\((4xy)(2x^2y)(3xy)^3\)[/tex] step-by-step.
1. Expand [tex]\((3xy)^3\)[/tex]:
[tex]\((3xy)^3\)[/tex] means multiplying [tex]\(3xy\)[/tex] by itself three times:
[tex]\[(3xy) \times (3xy) \times (3xy) = 3^3 \times x^3 \times y^3 = 27x^3y^3.\][/tex]
2. Write the expression with expanded parts:
Now substitute back [tex]\(27x^3y^3\)[/tex] in the original expression:
[tex]\[(4xy)(2x^2y)(27x^3y^3).\][/tex]
3. Combine the coefficients:
Multiply the numerical coefficients:
[tex]\[4 \times 2 \times 27 = 216.\][/tex]
4. Combine the [tex]\(x\)[/tex] terms:
Add the exponents of [tex]\(x\)[/tex] from each part:
- [tex]\(4xy\)[/tex] has [tex]\(x^1\)[/tex],
- [tex]\(2x^2y\)[/tex] has [tex]\(x^2\)[/tex],
- [tex]\(27x^3y^3\)[/tex] has [tex]\(x^3\)[/tex].
Adding these exponents gives:
[tex]\[1 + 2 + 3 = 6.\][/tex]
So the [tex]\(x\)[/tex] term is [tex]\(x^6\)[/tex].
5. Combine the [tex]\(y\)[/tex] terms:
Add the exponents of [tex]\(y\)[/tex] from each part:
- [tex]\(4xy\)[/tex] has [tex]\(y^1\)[/tex],
- [tex]\(2x^2y\)[/tex] has [tex]\(y^1\)[/tex],
- [tex]\(27x^3y^3\)[/tex] has [tex]\(y^3\)[/tex].
Adding these exponents gives:
[tex]\[1 + 1 + 3 = 5.\][/tex]
So the [tex]\(y\)[/tex] term is [tex]\(y^5\)[/tex].
6. Final Simplified Expression:
So, the simplified form of the expression is:
[tex]\[216x^6y^5.\][/tex]
Thus, the answer is [tex]\(216x^6y^5\)[/tex].
1. Expand [tex]\((3xy)^3\)[/tex]:
[tex]\((3xy)^3\)[/tex] means multiplying [tex]\(3xy\)[/tex] by itself three times:
[tex]\[(3xy) \times (3xy) \times (3xy) = 3^3 \times x^3 \times y^3 = 27x^3y^3.\][/tex]
2. Write the expression with expanded parts:
Now substitute back [tex]\(27x^3y^3\)[/tex] in the original expression:
[tex]\[(4xy)(2x^2y)(27x^3y^3).\][/tex]
3. Combine the coefficients:
Multiply the numerical coefficients:
[tex]\[4 \times 2 \times 27 = 216.\][/tex]
4. Combine the [tex]\(x\)[/tex] terms:
Add the exponents of [tex]\(x\)[/tex] from each part:
- [tex]\(4xy\)[/tex] has [tex]\(x^1\)[/tex],
- [tex]\(2x^2y\)[/tex] has [tex]\(x^2\)[/tex],
- [tex]\(27x^3y^3\)[/tex] has [tex]\(x^3\)[/tex].
Adding these exponents gives:
[tex]\[1 + 2 + 3 = 6.\][/tex]
So the [tex]\(x\)[/tex] term is [tex]\(x^6\)[/tex].
5. Combine the [tex]\(y\)[/tex] terms:
Add the exponents of [tex]\(y\)[/tex] from each part:
- [tex]\(4xy\)[/tex] has [tex]\(y^1\)[/tex],
- [tex]\(2x^2y\)[/tex] has [tex]\(y^1\)[/tex],
- [tex]\(27x^3y^3\)[/tex] has [tex]\(y^3\)[/tex].
Adding these exponents gives:
[tex]\[1 + 1 + 3 = 5.\][/tex]
So the [tex]\(y\)[/tex] term is [tex]\(y^5\)[/tex].
6. Final Simplified Expression:
So, the simplified form of the expression is:
[tex]\[216x^6y^5.\][/tex]
Thus, the answer is [tex]\(216x^6y^5\)[/tex].
